Question

Solve each quadratic equation. Show your work. 14. (2x – 1)(x + 7) = 0 15. x2 + 3x = 10 16. 4x2 = 100

Answer 1

14. (2x - 1)(x + 7) = 0

Using the zero factor property, we know that either the first or second terms (or both) must be equal to 0 if their product is 0. We can set each term equal to 0 to find the solutions:

2x - 1 = 0
2x = 1
x = 1/2

x + 7 = 0
x = -7

15.
`x^(2) +3x=10`

To solve this equation, you first need to set it equal to 0:


`x^(2) +3x=10 \\ x^(2) +3x-10 = 0`

Next, it can be factored:


`x^(2) +3x-10 = 0 \\ (x+5)(x-2)=0`

Finally, we can solve just like we did above:

x + 5 = 0
x = -5

x - 2 = 0
x = 2

16.
`4x^2=100`

First, you can simplify by dividing each side by 4:


`4x^2=100 \\ x^2=25`

Now, set the equation equal to 0:


`x^2=25 \\ x^2-25=0`

Next, factor:


`x^2-25=0 \\ (x+5)(x-5)=0`

Finally, find the solutions:

x + 5 = 0
x = -5

x - 5 = 0
x = 5